Untitled Document

Question Bank No: 1

1. X linear strain is produced in a wire of elasticity coefficient Y.The stored potential energy in unit volume of this wire is

a)		Y $x^{2}$
b)		2Y $x^{2}$
c)		$\frac{1}{2} y^{2} x$
d)		$\frac{1}{2} {yx}^{2}$

2. There is a horizontal film of soap solution.On it, a thread is placed in the form of a loop.The film is pierced inside the loop and the thread becomes a circular loop of radius R.If the surface tension of the loop be T, what will be the tension in the thread?

a)		RT
b)		2 $π RT$
c)		$π R^{2} T$
d)		$π R^{2} / T$

3. The amount of work done in blowing a soap bubble such that its diameter increases from d to D is (S=surface tension of solutions)

a)		$π (D^{2} - d^{2}) S$
b)		2 $π (D^{2} - d^{2}) S$
c)		4 $π (D^{2} - d^{2}) S$
d)		8 $π (D^{2} - d^{2}) S$

4. When a 4kg mass is hing vertically on a light spring that obeys Hooke' law, the spring stretches by 2 cm.The work required to be done by an external agent in stretching this spring by 5cm will be

a)		0.245J
b)		0.495J
c)		2.450J
d)		4.900J

5. A wire of length L and radius r rigidly fixed at one end. On stretching the other end of the wire with a force F,the increase in its length is l.If another wire of same material but of length 2L and radius 2r is stretched with a force 2F,the increase in its length will be

a)		l/4
b)		l/2
c)		l
d)		2l

6. If the pressure in a closed vessel is reduced by drawing out some of the gas, the mean free path of two molecules

a)		is increased
b)		is decreased
c)		remains unchanged
d)		increases or decreases according to the nature of gas

7. To expel half the mass of air from a large flask at $27^{0} C$ it must be heated to

a)		$54^{0} C$
b)		$177^{0} C$
c)		$277^{0} C$
d)		$327^{0} C$

8. If the masses of all molecules of a gass are halved and their speeds doubled,then the ratio of initial and final pressure would be

a)		2:1
b)		1:2
c)		4:1
d)		1:4

9. A hole is made at the bottom of a tank filled with water (p= $10^{3} kg / m^{3}) .$ If the total pressure at the bottom of the tank is three atmosphere(1 atm = $10^{5} N / m^{2})$ then the velocity of efflux is

a)		$\sqrt{400 m / s}$
b)		$\sqrt{200 m / s}$
c)		$\sqrt{600 m / s}$
d)		$\sqrt{500 m / s}$

10. In a laminar flow the velocity of the liquid in contact with the walls of the tube is

a)		Zero
b)		maximum
c)		in between Zero and maximum
d)		equal to critical velocity

11. A volume V of a viscous liquid flows per unit time due to a pressure head $Δ p$ along a pipe of diameter d and length L.Instead of this pipe, a set of four pipes each of diameter d/2 and length 2L is connected to the same pressure head $Δ p .$ Now the volume of liquid flowing per unit time is

a)		V/16
b)		V/8
c)		V/4
d)		V

12. If the velocity of the fluid is the same at a given point at all times, then the flow is

a)		turbulent
b)		rapid
c)		viscous
d)		streamlined

13. A piece of ice is floating in a beaker containing water. When ice melts, the temperature falls from $4^{0} C$ to $1^{0} C .$ Then the level of water

a)		rises
b)		falls
c)		unchanged
d)		none of these

14. A wooden ball of density D is immersed in water of density d to a depth h below the surface of water and then released upto what height will the ball jump out of water?

a)		$\frac{d}{D} h$
b)		$(\frac{d}{D - 1}) h$
c)		h
d)		Zero

15. Asteel ball is floating in a trough of mercury.If we fill the empty part of the trough with water,what will happen to the steel ball?

a)		It will continue in its position
b)		It will move up
c)		It will move down
d)		It will execute vertical Oscillations

16. A soap bubble in vacuum has a radius of 3 cm and another soap bubble in vaccum has a radius of 4 cm.If the two bubbles coalesce under isothermal conditional then the radius of the new bubble is

a)		2.3cm
b)		4.5cm
c)		5cm
d)		7cm

17. A needle is 7.5 cm long.Assuming that needle is not wetted by water,how heavy can it be and still floated on water? (T=70 dyne/cm)

a)		1.07 gm cot
b)		1.07 N
c)		1.07dyne
d)		1.0 kg cot

18. In a surface tension experiment with a capillary tube water rises upto 0.1.If the same experiment is repeated in an artificial satellite which is revolving around the earth,water will rise in the capillary tube upto a height of

a)		0.1m
b)		0.2m
c)		0.98m
d)		full length of tube

19. If C is the radius of the sphere of influence of a liquid, then the thickness of the surface film is equal to

a)		C
b)		2C
c)		C/2
d)		Zero

20. A cable breaks if stretched by more than 2 mm.It is cut into two equal parts. By how much either part can be stretched without breaking?

a)		0.25mm
b)		0.5mm
c)		1mm
d)		2mm

21. Young's modules of brass and steel respectively 10 $\times 10^{10} N / m^{2}$ and 2 $\times 10^{10} N / m^{2} .$ A brass wire and a steel wire of the same length are extended by 1mm under the same force,the radii of brass and steel wires are $R_{B}$ and $R_{s}$ respectively,then

a)		$R_{S} = \sqrt{2 R_{B}}$
b)		$R_{S} = \frac{R_{B}}{\sqrt{2}}$
c)		$R_{S} = 4 R_{B}$
d)		$R_{S} = \frac{R_{B}}{4}$

22. An Indian rubber cord 10 m long is suspended vertically.How much does it stretch under its own weight? (p=1500kg/ $m^{3}, y = 5 \times 10^{8}$ N/ $m^{2} g = 10 m / s^{2}$ )

a)		15 $\times 10^{- 4} m$
b)		15 $\times 10^{- 2} m$
c)		15 $\times 10^{- 3} m$
d)		None of these

23. A beam of metal supported at the two ends is loaded at the centre.The depression at the centre is proportional to

a)		$y^{2}$
b)		y
c)		$(\frac{1}{y})$
d)		$(\frac{1}{y^{2}})$

24. When an air bubble rises from the bottom of a lake to the surface, its radius trebles.If the atmospheric pressure is equal to a column of mercury of height H meter,then the depth of the lake is (in meters) (sp.gravity of mercury =13.6)

a)		1.91 H
b)		189.6 H
c)		353.6 H
d)		367.2 H

25. The weight of a rubber tube is $w_{1},$ When empty and $w_{2}$ when filled with air at almost atmospheric pressure. The weight of air in the tube is w.Which of the following is incorrect?

a)		$w_{2} = w_{1} + w$
b)		$w_{2} < w_{1} + \frac{w}{2}$
c)		$w_{2} = w_{1}$
d)		$w_{1} < w_{2} + \frac{w}{2}$

26. Liquid rises to a height of 2 cm in a capillary tube. The angle of contact between the solid and the liquid is zero. The tube is depressed more now so that the top of capillary is only 1 cm above the liquid then the apparent angle of contact between the solid and the liquid is

a)		$0^{\circ}$
b)		$30^{\circ}$
c)		$60^{\circ}$
d)		$90^{\circ}$

27. At $27^{\circ} C$ temperature, the kinetic energy of an ideal gas is $E_{1}$ . If the temperature is increased to $327^{\circ}$ C, then kinetic energy would be

a)		$E_{1} / 2$
b)		$E_{1} / \sqrt{2}$
c)		$\sqrt{2} E_{1}$
d)		${2 E}_{1}$

28. The density of ice is 0.9 g/cc and that of sea water is 1.1 g/cc. An iceberg of volume V is floating in sea water. The fraction of iceberg above water level is

a)		1/11
b)		2/11
c)		3/11
d)		4/11

29. Two wires of equal lengths are made of same material. Wire A has a diameter that is twice as that of wire B. If identical weights are suspended from the ends of these wires, the increase in length is

a)		Four times for wire A as for wire B
b)		Twice for wire A as for wire B
c)		Half for wire A as for wire B
d)		One-fourth for wire A as for wire B

30. When a large bubble rises from the bottom of the lake to the surface, its radius doubles. If atmosphere is equal to that of column of water height H, then the depth of lake is

a)		8H
b)		7H
c)		2H
d)		H

31. During an experiment an ideal gas is found to obey an additional law ${VP}^{2}$ = constant. The gas is initially at temperature T and volume V, when it expands to volume 2V, the resulting temperature is

a)		$\frac{T}{2}$
b)		2T
c)		$\sqrt{2} T$
d)		$\frac{T}{\sqrt{2}}$

32. The root mean square velocity of $O_{2}$ at atmospheric pressure and at $0^{\circ} C$ is

a)		More than that of air
b)		Less than that of air
c)		Equal to that of air
d)		Nothing can be said

33. A polyatomic gas with n degrees of freedom has a mean energy per molecule is given by

a)		$\frac{nKT}{N}$
b)		$\frac{nKT}{2 N}$
c)		$\frac{nKT}{2}$
d)		$\frac{3 KT}{2}$

34. The unit of universal gas constant is

a)		Watt/K
b)		Gyne/C
c)		Erg/K
d)		Newton/R

35. A spherical body falling through a viscous liquid of infinite extent ultimately attains a constant value, when

a)		Upthrust + weight = viscous drag
b)		Weight +viscous drag = upthrust
c)		Viscous drag + upthrust = weight
d)		Viscous drag + upthrust > weight

36. In a turbulent flow, the velocity of the liquid molecules in contact with the walls of the tube is

a)		Zero
b)		Maximum
c)		Equal to critical velocity
d)		May have any value

37. We have three beakers A, B and C containing glycerine, water and kerosene respectively. They are stirred vigorously and placed on a table. The liquid which comes to rest at the earliest is

a)		Glycerine
b)		Water
c)		Kerosene
d)		All of them at the same time

38. More viscous oil is used in summer, than in winters in motors due to

a)		Rise in temperature in summer, the viscosity of oil decreases
b)		Rise in temperature in summer, viscosity of oil increases
c)		Surface tension of oil decreases
d)		Surface tension of oil increases

39. Viscosity of gas is

a)		About hundred times less than those of liquids
b)		About twenty times less than those of liquids
c)		About five hundred times less than those of liquids
d)		About ten hundreds times less than those of liquids

40. A body of density $d_{1}$ is counterpoised by Mg of weights of density $d_{2}$ in air of density d. Then the true mass of the body is

a)		M
b)		M $(1 - \frac{d}{d_{2}})$
c)		M $(1 - \frac{d}{d_{1}})$
d)		M $\frac{(1 - d / d_{2})}{(1 - d / d_{1})}$

41. A raft of wood ( density 600 kg/ $m^{3}$ ) of mass 120 kg floats in water. How much weight can be put on the raft to make it just sink?

a)		120 kg
b)		200 kg
c)		40 kg
d)		80 kg

42. An inverted bell lying at the bottom of a lake 47.6 m deep has 50 ${cm}^{3}$ of air trapped in it. The bell is brought to the surface of the lake. The volume of the trapped air will be (atmospheric pressure = 70 cm of Hg and density of 13.6 g/cc

a)		350 ${cm}^{3}$
b)		300 ${cm}^{3}$
c)		250 ${cm}^{3}$
d)		22 ${cm}^{3}$

43. Liquid drops are falling slowly one by one from vertical glass tube. Establish a relation between the weight W of the drop, the surface tension T and the radius r of tube ( $θ$ = $0^{\circ}$ )

a)		W = $π r^{2} T$
b)		W =2 $π rt$
c)		W = 2 $π r^{2} T$
d)		W = $\frac{4}{3} π r^{3} T$

44. If the work done in blowing a soap bubble of volume V is W, then the work done in blowing a soap bubble of volume 2V will be

a)		W
b)		2W
c)		$\sqrt{2}$ W
d)		W (4) 1/3

45. In which case, there is a maximum extension in the wire, if the same force is applied on each wire?

a)		L = 500 cm , d = 0.5 mm
b)		L = 200 cm , d = 0.2 mm
c)		L = 300 cm , d = 0.3 mm
d)		L = 400 cm , d = 0.1 mm

46. A body of mass m = 10 kg is attached to a wire of length 0.3 m. Its breaking stress is
4.8 $\times$ $10^{7}$ N/ $m^{2}$ . The area of cross-section of the wire is $10^{- 6} m^{2}$ . What is the maximum angular velocity with which it can be rotated in the horizontal circle?

a)		4 rad/s
b)		8 rad/s
c)		1 rad/s
d)		2 rad/s

47. A material has Poisson's ratio 0.5. If a uniform rod of it suffers a longitudinal strain of
2 $\times 10^{- 3}$ , what is the % increase in volume?

a)		2 %
b)		4 %
c)		0 %
d)		5 %

48. A wire can be broken by applying a load of 20 kg wt. The force required to break the wire of twice the diameter is

a)		20 kg wt
b)		5 kg wt
c)		80 kg wt
d)		160 kg wt

49. A liquid is kept in a cylindrical vessel which is rotated along its axis. The liquid rises at the sides. If the radius of the vessel be 5 cm and the speed of rotation is 4 rev/s then the difference in the height of the liquid at the centre of the vessel and its sides is

a)		8 cm
b)		2 cm
c)		40 cm
d)		4 cm

50. Ice floats in an oil held in a vessel. When the ice melts, then the level of oil

a)		Remains unchanged
b)		Goes up
c)		Goes down
d)		Nothing certain can be asserted